On the Exchange of Sensible and Latent Heat Between the Atmosphere and Melting Snow

On the exchange of sensible and latent heat between the atmosphere and melting snow

Authors: Paul C. Stoy, Erich Peitzsch, David Wood, Daniel Rottinghaus, Georg Wohlfahrt, Michael Goulden, and Helen Ward

NOTICE: this is the author’s version of a work that was accepted for publication in Agricultural and Forest Meteorology. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Agricultural and Forest Meteorology, Volume 252, April 2018, DOI#10.1016/j.agrformet.2018.01.028

Stoy, Paul C. , Erich Peitzsch, David Wood, Daniel Rottinghaus, Georg Wohlfahrt, Michael Goulden, and Helen Ward. "On the exchange of sensible and latent heat between the atmosphere and melting snow." Agricultural and Forest Meteorology 252 (April 2018): 167-174. DOI:10.1016/j.agrformet.2018.01.028.

Made available through Montana State University’s ScholarWorks scholarworks.montana.edu On the exchange of sensible and latent heat between the atmosphere and T melting snow ⁎ Paul C. Stoya, , Erich Peitzschb,c, David Wooda,c, Daniel Rottinghausa, Georg Wohlfahrtd, Michael Gouldene, Helen Wardf,g a Department of Land Resources and Environmental Sciences, Montana State University, Bozeman, MT, USA b Department of Earth Sciences, Montana State University, Bozeman, MT, 59717 USA c U.S. Geological Survey Northern Rocky Mountain Science Center, Bozeman, MT, 59717, USA d Institute of Ecology, University of Innsbruck, Sternwartestrasse 15, 6020 Innsbruck, Austria e Department of Earth System Science, University of California, Irvine, Irvine, CA, 92697, USA f Department of Meteorology, University of Reading, Reading, RG6 6BB, United Kingdom g Institute of Atmospheric and Cryospheric Sciences, University of Innsbruck, 6020 Innsbruck, Austria

ABSTRACT

The snow energy balance is diﬃcult to measure during the snowmelt period, yet critical for predictions of water yield in regions characterized by snow cover. Robust simpliﬁcations of the snowmelt energy balance can aid our understanding of water resources in a changing climate. Research to date has demonstrated that the net tur-

bulent ﬂux (FT) between a melting snowpack and the atmosphere is negligible if the sum of atmospheric vapor

pressure (ea) and temperature (Ta) equals a constant, but it is unclear how frequently this situation holds across different sites. Here, we quantified the contribution of FT to the snowpack energy balance during 59 snowmelt periods across 11 sites in the FLUXNET2015 database with a detailed analysis of snowmelt in subarctic tundra near Abisko, Sweden. At the Abisko site we investigated the frequency of occurrences during which sensible heat flux (H) and latent heat flux (λE) are of (approximately) equal but opposite sign, and if the sum of these terms,

FT, is therefore negligible during the snowmelt period. H approximately equaled -λE for less than 50% of the melt

period and FT was infrequently a trivial term in the snowmelt energy balance at Abisko. The reason is that the

relationship between observed ea and Ta is roughly orthogonal to the “line of equality” at which H equals -λE as warmer Ta during the melt period usually resulted in greater ea. This relationship holds both within melt periods

at individual sites and across diﬀerent sites in the FLUXNET2015 database, where FT comprised less than 20% of

the energy available to melt snow, Qm, in 44% of the snowmelt periods studied here. FT/Qm was signiﬁcantly −2 related to the mean ea during the melt period, but not mean Ta, and FT tended to be near 0 W m when ea

averaged ca. 0.5 kPa. FT may become an increasingly important term in the snowmelt energy balance across many global regions as warmer temperatures are projected to cause snow to melt more slowly and earlier in the

year under conditions of lower net radiation (Rn). Eddy covariance research networks such as Ameriﬂux must improve their ability to observe cold-season processes to enhance our understanding of water resources and surface-atmosphere exchange in a changing climate.

1. Introduction Leathers, 1999; Hayashi et al., 2005; Pederson et al., 2013), and snowmelt is projected to occur earlier and more slowly in a warming Quantifying the snowpack energy balance is critical for water reg- climate under conditions of lower net radiation earlier in the season ulation and runoff prediction (Dettinger et al., 2015; Kay and Crooks, (Musselman et al., 2017). To understand how snowmelt responds to 2014; Marks et al., 2008; Troin et al., 2016), avalanche forecasting climate variability, we must understand mass and energy fluxes to and (Slaughter et al., 2009; Wever et al., 2016), and predicting changes to from the snowpack, including key relationships that can simplify future snowpack persistence (Abatzoglou et al., 2014; Pederson et al., models without impacting their skill. 2011). Interannual variability in weather and climate change impact Using the convention that energy flux into the snowpack is positive, the timing and magnitude of snowmelt (Cline, 1997; Grundstein and the energy available to melt snow, Qm, is a function of the net radiation − λ “ ” (Rn, i.e. incident minus outgoing shortwave and longwave radiation), which H = E, hereafter the line of equality , and derived below in sensible heat flux (H), latent heat flux (λE), ground heat flux (G), and Methods. It is unclear if other melting snowpacks experience similar fl any energy ux due to precipitation (P, Marks and Dozier, 1992; Burns average climate conditions that make FT negligible during the melt et al. 2014): period and therefore when Rn measurements alone provide an accurate approximation of Qm (Eq. (1), noting that the magnitude of G is often Q + Q = R + H + λE + G + P = R + F + G + P. (1) m cc n n T trivial compared to other terms in Eq. (1) during snowmelt. Here, we quantify the contribution of FT to Qm during two snowmelt Qcc, the energy required to bring snow temperature to melting temperature (often called the cold content), is assumed here to be 0 W periods at a subarctic tundra research site near Abisko, Sweden and 59 −2 snowmelt periods across 11 eddy covariance study sites in the m when the snowpack is melting. The net turbulent flux, FT, is the sum of H and λE, the latter being of particular interest to snow science FLUXNET2015 database (Pastorello et al., 2017) to quantify the range as it represents sublimation and evaporation from and condensation to of meteorological conditions encountered during the melt period in ff the snowpack, and is thus connected to the snow mass balance.Hand di erent snowpacks. We examined two questions. First, are the micrometeorological conditions during the snowmelt period observed in λE tend to be minor but nontrivial contributions to Qm (Boon, 2009; ff Cline, 1997; Harding and Pomeroy, 1996; Fitzpatrick et al. 2017; Marks Welch et al. (2016) common for various sites with di erent physical and Winstral, 2001) and are arguably more difficult to measure via, for characteristics? To address this question, we examined eddy covariance example, eddy covariance compared to the radiometers and heat flux and radiometric measurements of energy exchange between the snowpack and the atmosphere from sites in different climate zones. plates used to measure Rn and G (Arck and Scherer, 2002). Under- −2 Second, how frequently is FT approximately equal to 0 W m , and standing situations in which the contribution of FT to Qm is negligible what is the relative contribution of FT to Qm during the snowmelt period would dramatically simplify our ability to measure and model Qm. In a comparison of studies at alpine sites over portions of the melt across sites? To address this question we study the distribution of micrometeorological conditions during different melt events. The goal of period, Cline (1997) found that the contribution of Rn to Qm ranged this analysis is to gain a better understanding of conditions in which the from 0 to 100%, illustrating that FT can be both a negligible and snowmelt energy balance can be accurately approximated using dominant source of energy for snowmelt. FT can dominate Qm in arid radiometric observations to simplify measurements and models. We environments, especially in the early season before Rn reaches higher focus our discussion on the steps necessary to improve observations of values (Beaty, 1975; Hawkins and Ellis, 2007). The contribution of FT to cold season processes within surface-atmosphere flux networks like Qm can vary due to weather patterns (Cline, 1997; Grundstein and fl Leathers, 1999; Hayashi et al., 2005), wind speed (Mott et al., 2011; Ameri ux, and to improve observations of climate and surface-atmo- fl Pohl et al., 2006), and vegetation (Endrizzi and Marsh, 2010; Mahrt and sphere ux at snowmelt measurement networks like SNOTEL (snow- Vickers, 2005), which makes model simplification difficult. However, pack telemetry, Serreze et al., 1999). the time scales of these comparisons range from the entire snow covered period to less than a week, and it is unclear how frequently, and 2. Methods under which conditions, FT contributes negligibly to Qm when snow is melting. 2.1. Snow energy balance and turbulent flux during snowmelt Welch et al. (2016) used eddy covariance measurements in a Welch et al. (2016) present a relationship in which the input of H to montane continental snowpack in Montana, USA, and found that H was − the snowpack is equal to −λE (i.e. F =0Wm 2) when snow is only about 10% less than the magnitude of -λE, such that FT T −2 −2 melting. Briefly, H can be written following e.g. Kaimal and Finnigan (−3MJm ) provided a negligible contribution to Qm (97 MJ m ) when integrated over the entire melt period. They described a linear (1994): relationship between near-surface air temperature (T ) and atmospheric a ρCp H =−(TT) vapor pressure (ea) for conditions under which H = − λE (Fig. 1, i.e. FT ass − rH (2) =0Wm 2 and the Bowen ratio β = H/ λE = − 1) that results when −3 snow surface temperature (Tss) is at 0 °C when snow is melting. It was where ρ is the molar density of air measured in mol m , Cp is the fi −1 −1 noted that average Ta and ea during the melt period fell near the line at speci c heat of dry air (J mol K ), and rH is the resistance to heat -1 flux (s m ). H is positive when Ta exceeds Tss noting the convention here that energy flux from the atmosphere to the snowpack is positive; positive H denotes heat transport from the surface to the atmosphere in

conventional ﬂux studies. Welch et al. (2016) assumed that Tss is 0 °C (273.15 K) when snow was melting. Thus,

ρCpa T H = rH (3)

We note that Tss in Eq. (2) is the aerodynamic surface temperature, which is the temperature that inﬂuences turbulent ﬂow. The aerodynamic surface temperature is similar to radiative surface temperature if melting snow can be considered a smooth surface for the case of eddy covariance research sites, and is thus related to the outgoing longwave

radiation (LWout) following the Stefan-Boltzmann equation: 4 LWout = AεσTsr (4) where A is the view factor (assumed to be 1 for a melting snowpack on a Fig. 1. The atmospheric vapor pressure (e ) and temperature (T ) at which energy flux a a flat surface), σ is the Stefan-Boltzmann constant, ε is the emissivity of into snow from sensible heat (H) and losses from latent heat (λE) during snowmelt are equal (i.e. H=− λE) following Welch et al. (2016) for different elevations above sea snow (which changes as a function of snow characteristics, e.g. Hori level and therefore mean psychrometric constants (γ), which are a function of atmo- et al., 2006), and Tsr is the radiometric snow surface temperature in spheric pressure with minor temperature dependency as discussed in Loescher et al. degrees Kelvin, 273.15 K if snow is melting. Aerodynamic and radio- (2009). The black shaded area denotes the region for which ea exceeds saturation over ice metric surface temperatures are otherwise different terms. ff following Go and Gratsch (1945). Like H, λE can be written: ρCp λE =−([]eeTass) γrv (5)

−1 where rv is the resistance to latent heat ﬂux (s m ), e[Tss] is the vapor pressure at the snow surface, and γ is the psychrometric constant. γ is not a true constant, and varies a function of atmospheric pressure (Pa) following e.g. Campbell and Norman (1998):

γ = CpPa/(0.622λ) (6) where 0.622 is the ratio of the molecular mass of water vapor to dry air. We note that γ exhibits minor temperature dependency assumed to be trivial here (Loescher et al., 2009). λE tends to be negative during the melt period (i.e. sublimation and evaporation to the atmosphere dominate condensation to the snowpack) because the melting and sublimating snow surface is saturated but the overlying air usually is not (Marks and Dozier, 1992; Reba et al.,

2009). Assuming again that Tss is 0 °C during the melt period, ea at saturation is 0.61173 kPa. Further, rv is similar to rH in the absence of Fig. 2. An example snowmelt period (gray shading) from the Neustift, Austria (AT-Neu) vegetation (Campbell and Norman, 1998) such that eddy covariance research site as determined by the shortwave albedo (subplot A) and

ρCp outgoing longwave radiation(LWout, subplot B). The melt period is considered to begin λE ≈−(ea 0.61173). when LWout reaches a local maximum after when shortwave albedo simultaneously begins γrH (7) to decline, and ends before LWout follows a clear diurnal pattern and shortwave albedo λ values are characteristic of a snow-free land surface. Only periods in which calculated Qm When H and E are assumed to be equal but opposite, the expression − are greater than 0 W m 2 within this period is considered the ‘melt period’ for the pur- can be simpliﬁed to yield a linear relationship between ea and Ta that γ poses of this analysis, and the implications of these assumptions regarding melt period varies as a function of (Welch et al., 2016) deﬁnition are discussed in the Discussion section.

γTa += ea 0.61173 (8) Netherlands). The beginning of the snowmelt period was defined as the Mean Ta and ea during the melt period can provide insight into the periods of consistent declines in observed snow depth (measured using dynamics of FT because Eq. (8) is linear, and we study both mean Ta and a Cambpell Scientific SR50 sonic distance sensor) in 2009. Snow depth ea during the entire melt period and their variability at the half-hourly time steps commonly used in eddy covariance studies. measurements were not available in 2008, and the beginning of the snowmelt period in 2008 is defined as the day at which measurements began after the tower power system was repaired on April 10, 2008 2.2. Study sites: selection criteria following damage the previous winter. LWout observations were un- fortunately not available at the Abisko site, and we instead define Difficulties arise when measuring the energy balance of melting periods of melting snow within the defined snowmelt periods as those snow below forest canopies where the well-developed turbulence fa- − for which calculated Q was greater than 0 W m 2. We discuss the vored for eddy covariance measurements is rarely encountered (Misson m consequences of these assumptions in the Discussion section. et al., 2007; Staebler and Fitzjarrald, 2004). In addition, canopies can lead to a decoupling of sub-canopy and above-canopy fluxes (Burns et al., 2014; Jocher et al., 2017; Thomas et al., 2013), complicating the 2.2.2. Study sites: FLUXNET2015 interpretation of results from flux towers, and requiring additional in- To avoid complications posed by vegetation measuring energy ex- strumentation to understand snow versus canopy impacts on surface- change between a melting snowpack and the atmosphere, we study sites atmosphere exchange (although see: Molotch et al., 2007; Burns et al., characterized as grasslands, croplands, or open shrublands in the 2014; Welch et al., 2016). We focused our study on sites in pre- FLUXNET2015 database and attempt to avoid situations of emerging dominately open areas or open canopies in which the exchange of en- vegetation as described in Fig. 2. The FLUXNET2015 sites studied here ergy between the snow itself and the atmosphere can be measured more included energy balance measurements (Eq. (1) including eddy covar- readily iance measurements of H and λE and radiometric observations of Tss (via outgoing longwave radiation) as well as standard Ta and RH 2.2.1. Study sites: Abisko, Sweden measurements in areas with distinct snow accumulation and ablation The Abisko, Sweden subarctic tundra research site is at an elevation seasons, differing climate types (Kottek et al., 2006), and elevations of 752 m above sea level at 68.299 N, 18.847 E (Fox et al. 2008; Stoy (Table 1). Measurement details are noted in the references associated et al., 2012, 2013). H was measured using a Gill R3 sonic anemometer with each site and listed in Table 1. Snowmelt periods were defined by and λE was measured using the eddy covariance approach by coupling quantifying periods with declining shortwave albedo and near-constant the anemometer with a LI-COR 7500 infrared gas analyzer (Li-Cor, LWout as demonstrated in Fig. 2. The explicit assumption with this ap- Lincoln, Nebraska, U.S.A), both at 3 m above the ground surface. Half- proach is that albedo decreases during snowmelt, be it due to the ap- hourly fluxes were calculated using FluxView (Centre for Ecology and pearance of impurities and/or changes in grain size (e.g. Warren,

Hydrology, Wallingford, U.K.) as described in more detail in Stoy et al. 1984), and that near-constant LWout reflects a snowpack that is melting (2013). H and λE observations that did not meet a turbulence intensity with minimal changes in Qcc. Only melt periods that occurred over the −1 threshold of a friction velocity (u*) of greater than 0.08 m s de- course of multiple days and without energy input from precipitation termined using CO2 flux observations were excluded from the analysis. events are examined here. We likewise only study periods with mea- Ta and relative humidity (RH) were measured using a HMP45 sensor sured (not gapfilled) turbulent fluxes during periods when −2 (Vaisala, Helsinki, Finland), at a height of 2 m. ea was calculated from Qm >0Wm as at the Abisko study site. G has been found to be Ta and RH measurements as described in Section 2.4. negligible in most locations with snow cover (Boike, 2003; Cline, 1997; Snow presence was estimated using observations of reflected Welch et al., 2016) and was assumed to be zero. The consequences of shortwave radiation measured at 2 m using a downward-facing CM11 these assumptions are discussed in the Discussion section. We then secondary standard pyranometer (Kipp and Zonen, Delft, The calculated the relative contributions of FT and Rn to Qm using Eq. (1). −2 Table 1 and mean Qm was on the order of 20 W m such that FT could not be The latitude, longitude, elevation (above sea level) and International Geosphere- excluded from the energy balance Eq. (1) for a robust estimate of Qm. fi Biosphere Programme (IGBP) vegetation classi cation for FLUXNET2015 research sites The distribution of H during the melt period of 2008 had a heavy with albedo and outgoing longwave radiation measurements to estimate melt periods following Fig. 2. CRO: crop; GRA: grass; OSH: open shrub; WET: wetland. *Three nearby tail toward negative values (indicating surface heating) (Fig. 4A), which agricultural fields are measured near Mead, Nebraska. We choose the site US-Ne1 as resulted in a similar distribution of FT (Fig. 4B), noting that peak FT − representative for all three. occurred near 0 W m 2 in both 2008 and 2009. Latent heat loss from the snowpack (negative values in Fig. 4C) dominated positive values Site Lat Long Elevation (m IGBP Reference (indicating condensation) during both melt periods. The distribution of asl) β had a minor peak near −1 (the value at which H = − λE) during AT-Neu 47.1167 11.3175 970 GRA Wohlfahrt et al. (2008) 2008 and a relatively high density of observations of β near -1 in 2009. CH-Fru 47.1158 8.5378 982 GRA Eugster and Zeeman The analysis of mean values during the melt period and individual half- (2006) hourly points both indicate that conditions frequently occur in which F CZ-wet 49.0247 14.7704 426 WET T DE-Geb 51.1001 10.9143 162 CRO Anthoni et al. (2004) is negligible, but also that the full melt period cannot be assumed to DE-Gri 50.9495 13.5125 385 GRA Owen et al. (2007) have negligible FT. DE-Kli 50.8929 13.5225 478 CRO Owen et al. (2007) DE-SfN 47.8064 11.3275 590 WET Hommeltenberg et al. (2014) 3.2. Snowmelt at FLUXNET2015 research sites FI-Lom 67.9972 24.2092 274 WET Aurela et al. (2009) IT-MBo 46.1047 11.0458 1550 GRA Marcolla et al. (2011) Snowmelt periods at the FLUXNET2015 research sites (Table 1) IT-Tor 45.8444 7.5781 2160 GRA Migliavacca et al. (2011) were determined by examining LWout and albedo time series as de- US-Ne1* 41.1651 −96.4766 361 CRO Verma et al. (2005) monstrated in Fig. 2. Mean Ta across all sites during the defined melt period was 2.6 °C and mean ea was 0.56 kPa (Fig. 5). Mean Ta was significantly related to ea (p = 0.001) and explained 24% of the varia- We note that snowmelt periods estimated within the footprint of the bility of ea such that the distribution of observed Ta and ea was ap- fl radiometer and those measured by the eddy covariance ux footprint proximately orthogonal to the line of equality (Fig. 5). are likely to be different, and discuss strategies for observing cold FT comprised between -96% (i.e. of opposite sign than Rn) and 108% season processes in tower measurement networks in the Discussion of Qm across the 60 FLUXNET2015 melt periods studied (Fig. 6) and its section. absolute value was less than 15% of Qm on 22 instances, in other words during 37% of the melt periods studied. If uncertainty in eddy covar- 2.3. Calculation of variables iance measurements can be assumed to be on the order of 10–20% (e.g.

Goulden et al., 1997), there are many examples in which FT need not be For each site we used RH and Ta recorded during the snowmelt measured for a robust estimate of Qm given observational uncertainties, period to quantify ea and calculated the saturated vapor pressure es(Ta) but these instances are in the minority of the snowmelt periods studied ff over ice for a given temperature using the Go and Gratch (1945) here. The ratio FT/Qm was not related to variability in mean Ta during equation: the melt periods (p = 0.35), but was significantly related to mean ea (p = 0.0002), which explained 21% of its variability. The point at log10 esa( T )=− 9.09718(TT0 /a− 1) − 3.56654log10 ( T00 / Ta )+ 0.876793(1 −TT / ) −2 which FT/Qm crossed 0 (i.e. FT =0Wm ) occurred when ea was ap- * + log10 ei0 (9) proximately 0.5 kPa. * where T0 is the triple point temperature of water (273.16 K) and ei0 is the saturated vapor pressure of water at 0 °C in hPa (6.1173 hPa). ea 4. Discussion was then calculated by multiplying RH (as a fraction) by es. As our sites varied in elevation, we calculated γ using The objectives of this study were to examine flux and micro- −3 meteorological measurements across multiple sites and snowmelt per- γP=×0.665 10 a (10) iods to identify periods when FT is a minor input to Qm. The “line of Average Pa as a function of elevation above sea level (h, see Table 1) equality” when this situation should theoretically occur was rarely was calculated using encountered within or among melt periods. Instead, observed mean

5.26 melt-period ea and Ta observations were approximately orthogonal to ⎛ 293− 0.0065h ⎞ Pa = 101.3 the line of equality as warmer Ta coincided with higher values of ea in ⎝ 293 ⎠ (11) snowmelt-dominated landscapes (Fig. 3 and 5). Because ea tends to be following e.g.Zhu et al. (2012). β was calculated as H/λE excluding near its saturated value during snowmelt across the sites studied here, λ −2 −2 periods for which the absolute value of E was less than 1 W m . the point at which FT is predicted to be 0 W m tended to occurs when ea was on the order of 0.5 kPa and therefore Ta on the order of 1–2°C 3. Results with minor sensitivities to h and thereby Pa (Fig. 1). Of course, inﬂuxes of warm and dry air (Cline, 1997; Grundstein and Leathers, 1999) such 3.1. Snowmelt at Abisko as Föhn winds and Chinooks (Desai et al., 2016; Hayashi et al., 2005; MacDonald et al., 2018; Zeeman et al., 2017) or other synoptic-scale The snowmelt events during both 2008 and 2009 at Abisko began patterns (Grundstein and Leathers, 1999) can result in situations where during the second week of April and ended on May 3, 2008 and April ea is not near saturation and greatly increases the energy available to 24, 2009, respectively (Table 2). Ta, ea, and Rn were, on average, melt snow by increasing both Ta and the gradient in moisture to support greater during the 2008 melt period (Table 2), which extended until λE, thus deviating from the general trend that ea is related to Ta during May when Rn was greater. Mean Ta and ea fell to the warmer side of the melt. Observing energy exchange between melting snowpacks and the line of equality in 2008, conditions which theoretically favor greater H atmosphere across multiple sites continues to be a challenge because over the magnitude of λE (Welch et al., 2016), and the cooler side in measurement networks are not optimized to observe either cold season 2009. Observations, however, suggested that the magnitude of λE was processes or surface-atmosphere exchange. We brieﬂy discuss the greater than H in 2008 and less than H in 2009 (Table 2). The magni- Abisko and FLUXNET2015 results, and then outline the steps necessary −2 tude of mean FT was greater than 10 W m during both melt periods, to improve observations of cold season processes by research networks. Table 2

The start date and end dates of study snowmelt periods at a subarctic tundra site in Abisko, Sweden, deﬁned as periods for which energy available to melt snow (Qm) was greater than −2 0Wm with mean air temperature (Ta), atmospheric vapor pressure (ea), energy available to melt snow (Qm), net radiation (Rn), and the net turbulent ﬂux (FT) of sensible heat (H) and latent heat.

−2 −2 −2 −2 −2 Year Start date End date Mean Ta (°C) Mean ea (kPa) Mean Qm(W m ) Mean Rn(W m ) Mean FT(W m ) Mean H(W m ) Mean λE(W m )

2008 April 11 May 3 3.0 0.57 19 35 −16 7 −22 2009 April 10 April 24 0.5 0.49 20 5 15 34 −19

Fig. 3. Air temperature (Ta) and atmospheric vapor pressure (ea) during the 2008 and Fig. 5. Mean air temperature (Ta) and atmospheric vapor pressure (ea) during snowmelt 2009 snowmelt periods for a tundra site in Abisko, Sweden with half hourly measure- periods defined using outgoing longwave radiation and shortwave albedo observations ments as small dots and mean values during snowmelt as large symbols with error bars (1 following Fig. 3 for FLUXNET2015 sites with multi-day melt periods and short statured standard deviation). The solid black line represents the relationship between temperature vegetation (Table 1). The solid black line represents the relationship between temperature and atmospheric vapor pressure where the net turbulent flux between snowpack and and atmospheric vapor pressure where the net turbulent flux between snowpack and atmosphere is equal under conditions when the snow surface temperature is 0 °C at the atmosphere is equal under conditions when the snow surface temperature is 0 °C at an elevation of the Abisko site (752 m asl) and the black shaded area denotes the region for elevation of 752 m asl following Fig. 3 for reference. which ea exceeds saturation over ice following Goff and Gratsch (1945) (Eq. (9)).

16 A B 0.04 0.04 14 ) T

p(H) 12 0.02 p(F 0.02 10 0 0 -200 0 200 -200 0 200 8 H (W m-2) F (W m-2) T 6

4 C 2008 D 0.04 0.04 2009 2 ) E) p(

p( 0.02 0.02 0 -1 -0.5 0 0.5 1

0 0 -200 0 200 -10 0 10 Fig. 6. The ratio between the mean turbulent ﬂux (FT) and energy available to melt snow -2 E (W m ) (Qm) during 59 melt periods across 11 FLUXNET2015 research sites described in Table 1.

Fig. 4. The probability distributions of half hourly measurements of sensible heat flux (H, λ “ ” panel A), the sum of turbulent fluxes (FT, B), the latent heat flux (λE, C), and the Bowen exceed that of E when average meteorological conditions fell above ratio (β, D) during two snowmelt periods for a subarctic tundra site near Abisko, Sweden. (warmer and moister than) the line of equality. This is likely because − Latent heat flux measurements with an absolute value less than 1 W m 2 were excluded the assumption that a reflective surface (indicating snow) near the flux β from the calculation of . The solid vertical lines represent the ordinate and the dashed tower was not necessarily indicative of consistent snow cover across the vertical line in D represents a β value of −1. turbulent flux footprint, which extends to the order of tens to hundreds of meters depending on atmospheric stability (Fox et al., 2008; Stoy 4.1. Abisko et al., 2013). It is likely in the case of the Abisko measurements that the footprint Measurements at Abisko highlighted the notion that FT can often be of the radiometer and sonic distance sensor used to define the begin- −2 fi near 0 W m when Qm is positive, but also that the simpli cation ning and end of the snowmelt period were poor approximations of found by Welch et al. (2016) should not be transferred to different sites continuous snow presence within the eddy covariance flux footprint. and melt periods as FT was a nontrivial term in Qm during both melt The Abisko site is characterized by patchy vegetation (Fletcher et al., periods. Results also opposed the notion that the magnitude of H should 2012; Spadavecchia et al., 2008; Stoy et al., 2013; Stoy and Quaife 2015). Vegetation patches, particularly of the moss Polytrichum pili- assumptions used here (Fig. 2) would benefit from more detailed ob- ferum, become exposed during the melt period and can even exhibit servations of temperature within the snowpack, including its cold positive photosynthetic carbon uptake adjacent to and even under content, as well as more detail about the cause of the albedo decrease, snow-covered patches (Street et al., 2012). Mosses tend to partition be it impurities (e.g. Conway et al., 1996) and/or increases in grain size energy into H as they lack vascular tissue to transport water (Liljedahl during melt (Wiscombe and Warren, 1980). et al., 2011), and evaporation will be hastened by locally warm vege- As was likely the case for the Abisko observations, there may be tation patches versus snow. Vegetation, even in situations where it is important differences in what is being observed by tower-mounted short-statured, can create spatial variability in snowmelt and influence radiometers and the eddy covariance system, which have different turbulent flux when it is protruding from the snow (Endrizzi and Marsh, observational footprints. Phenological cameras – properly positioned – 2010; Mahrt and Vickers, 2005; Mott et al., 2013). It is unclear how are adept at observing spatial patterns of snow within flux footprints positive G from these melting vegetation and bare ground patches in- (Julitta et al. 2014) in order to understand when turbulent fluxes arise fluence the surrounding energy balance, but our assumption that G is from a footprint that represents a matrix of melted and unmelted pat- − approximately 0 W m 2 during the melt period is not likely valid, ches (Mott et al., 2013), especially given that flux towers themselves especially towards the end of melt periods when the snowpack is can (unintentionally) behave as miniature snow fences and result in shallow and/or patchy. Complicated melt patterns within the flux minor accumulations that may influence radiometric measurements. footprint must be taken into account for an accurate understanding of Phenocam observations are increasingly common at eddy covariance melt processes, and we discuss how to do so in section 4.3. research sites (Migliavacca et al., 2011; Richardson et al., 2009), and flux networks will continue to benefit from their inclusion, noting that 4.2. FLUXNET2015 phenocams (best pointed north) likewise are unlikely to have a similar observational footprint to the eddy covariance sensors.

Mean Ta and ea across melt periods for the FLUXNET2015 sites A more complicated measurement recommendation to flux tower (Table 1 and Fig. 5) followed a positive relationship such that the point sites would be the addition of snow pillows as used in SNOTEL at which this relationship crossed the line of equality was on the order (SNOwpack TELemetry), which represent a larger cost and infra- of 1–2 °C and 0.5 kPa. In other words, there were many instances in structural investment, and may influence the non-snow covered flux which mean Ta and ea fell near the line of equality, but this was an footprint because they necessitate the removal of vegetation. The al- exception rather than the rule. With uncertainty of eddy covariance ternate solution is to manually measure snow mass and its changes over observations in mind, FT comprised less than 20% of Qm some 43% of time, which likewise often represents a sizeable investment and may be the time, but nearly 50% of the time when mean ea was between 0.5 kPa impractical or dangerous in many situations, especially when the risk of and 0.7 kPa. In summary, conditions in which FT is negligible exist avalanche activity is high and when travel over a landscape with during parts of snowmelt periods or even cumulatively during the en- melting snow becomes impractical. Larger infrastructural investments tire melt period (e.g. Welch et al., 2016), but at insufficient frequencies are also an option for studying snowmelt processes like condensation to justify not measuring or modeling turbulent fluxes for a full quan- and sublimation. For example Hood et al., (1999) measured turbulent fi fl ti cation of Qm (Fig. 1). The question then becomes: How do we to best ux at multiple heights and moved sensors as a function of snowpack make observations of cold season processes and integrate them into flux height, but these represent additional complexity for integration into and snow networks? flux networks. At a minimum, we recommend investments in depth sensors (which can also be used to measure vegetation height growth), 4.3. Improvements to micrometeorological networks to study the cold period noting that declines in snow depth may also correspond to wind-in- duced sublimation or settling. Phenological cameras, snow temperature Eddy covariance systems provide important information to quantify sensors, and heated multi-component radiometers (to avoid snow cov- the terms that contribute to Qm at high (usually half-hourly) temporal ered radiometers, and including upwelling shortwave and longwave resolution, but are rarely installed with cold season energy and water radiation measurements) improve our ability to observe cold-season flux processes in mind e.g. (Molotch et al., 2007; Reba et al., 2009; processes, with the strong suggestion that incorporating snow pillows Welch et al., 2016). Eddy covariance analyses can be greatly improved into existing eddy covariance sites will dramatically increase the ability by simple additions of distance sensors, which for short (e.g. grass and of snow observing networks like SNOTEL to interact with surface-at- crop) canopies also make for a nice automated measurement of canopy mosphere exchange measurement networks such as Ameriflux. height during the active period (Jonas et al., 2008). It is also critical to An additional recommendation to couple process-based studies of measure the cold content of the snowpack using temperature sensors snowmelt with observations is to add instrumentation to snow mea- within the snowpack to measure the cold season energy balance, and surement networks like SNOTEL. SNOTEL sites are critical for water doing so using thermocouples incurs minimal added expense. Qcc can be resource management (Serreze et al., 1999), long-term studies of hy- non-zero even within melt periods (Burns et al., 2014), but in the ab- drology (Bedford and Douglass, 2008), model validation (Coughlan and sence of snow temperature measurements it was necessary to assume Running, 1997) and more, but rarely if ever include atmospheric hu- that Qcc was negligible for the purposes of this analysis. Automated midity sensors or radiometers that are critical for understanding the ffi snow temperature sensors are an e cient way to test the validity of this mechanisms that drive Qm. By adding instrumentation to eddy covar- assumption and better measure all terms in Eq. (1). iance networks to improve their ability to observe cold season pro- Without additional infrastructure, assumptions regarding snow cesses, and to snow measurement networks to improve process-based presence and melting are necessary, and may or may not be robust. Our studies, our ability to measure and model snow on a changing planet assumption that decreases in albedo correspond to the beginning of the will be improved. melt period (e.g. Fig. 2) is an approximation that corresponds to known changes in snow albedo during melt due to changes in snow grain size 5. Conclusion and the melting of snow around impurities within the snowpack (e.g.

Warren, 1984). Likewise, we assume that large changes in Qcc during re- Observations demonstrate that the micrometeorological conditions freezing can be assumed to be minimal if the snow surface stays near that lead to periods when H = − λE during snowmelt occur infre-

0 °C, which can be observed using LWout. The notion that snowmelt quently because ea tends to increase with Ta in landscapes characterized fl − λ occurs under relatively invariant LWout re ects the assumption that the by melting snow. There are times when H = E during the snowmelt Qcc is minimal during the melt period, but because refreezing occurs it period as found by Welch et al (2016), but these conditions did not fi must be quanti ed for a robust understanding of the melt period. Both result in a situation where FT was a negligible contribution to Qm at a subarctic tundra ecosystem near Abisko, Sweden and in less than half of Conway, H., Gades, A., Raymond, C.F., 1996. Albedo of dirty snow during conditions of – the snowmelt periods we examined in the FLUXNET 2015 database. In melt. Water Resour. Res. 32, 1713 1718. http://dx.doi.org/10.1029/96WR00712. summary, F needs to be measured and modeled for a robust under- Dettinger, M., Udall, B., Georgakakos, A., 2015. Western water and climate change. Ecol. T Appl. 25, 2069–2093. http://dx.doi.org/10.1890/15-0938.1. standing of snowmelt, but will frequently be a negligible term in the Desai, A.R., Wohlfahrt, G., Zeeman, M.J., Katata, G., Eugster, W., Montagnani, L., snowmelt energy balance. Mauder, M., Schmid, H.-P., 2016. Montane ecosystem productivity responds more to Networks of flux towers can be used to further improve our un- global circulation patterns than climatic trends. Environ. Res. Lett. 11 (2), 024013. http://dx.doi.org/10.1088/1748-9326/11/2/024013. derstanding of snowmelt, especially if snow-specific measurements like Endrizzi, S., Marsh, P., 2010. Observations and modeling of turbulent fluxes during melt snow temperature sensors or snow pillows are incorporated into flux at the shrub-tundra transition zone 1: point scale variations. Hydrol. Res. 41, 471. measurement networks, or even if multi-purpose instrumentation like http://dx.doi.org/10.2166/nh.2010.149. Eugster, W., Zeeman, M.J., 2006. Micrometeorological techniques to measure ecosystem- fl distance sensors or phenocams are included in ux measurement net- scale greenhouse gas fluxes for model validation and improvement. Int. Congr. Ser. works. Overall, our study illustrates the complexity of the energy bal- 1293, 66–75. ć ance during the snowmelt period at a variety of sites with low statured Fitzpatrick, N., Radi , V., Menounos, B., 2017. Surface energy balance closure and turbulent flux parameterization on a mid-latitude mountain glacier, purcell mountains, vegetation and the complexity of making these measurements, yet Canada. Front. Earth Sci. 5, 67. provides path forward for better understanding cold season processes in Fletcher, B.J., Gornall, J.L., Poyatos, R., Press, M.C., Stoy, P.C., Huntley, B., Baxter, R., a changing climate. Phoenix, G.K., 2012. Photosynthesis and productivity in heterogeneous arctic tundra: consequences for ecosystem function of mixing vegetation types at stand edges. J. Ecol. 100, 441–451. http://dx.doi.org/10.1111/j.1365-2745.2011.01913.x. Acknowledgements Fox, A.M., Huntley, B., Lloyd, C.R., Williams, M., Baxter, R., 2008. Net ecosystem exchange over heterogeneous arctic tundra: scaling between chamber and eddy covariance measurements. Global Biogeochem. Cycles 22, GB2027. http://dx.doi.org/ This work used eddy covariance data acquired and shared by the 10.1029/2007GB003027. FLUXNET community, including these networks: AmeriFlux, AfriFlux, Goff, J., Gratch, S., 1945. Thermodynamic properties of moist air. ASHVE Trans. 51, AsiaFlux, CarboAfrica, CarboEuropeIP, CarboItaly, CarboMont, 125–158. ChinaFlux, Fluxnet-Canada, GreenGrass, ICOS, KoFlux, LBA, NECC, Goulden, M.L., Daube, B.C., Fan, S.-M., Sutton, D.J., Bazzaz, A., Munger, J.W., Wofsy, S.C., 1997. Physiological responses of a black spruce forest to weather. J. Geophys. OzFlux-TERN, TCOS-Siberia, and USCCC. The FLUXNET eddy covar- Res. Atmos. 102, 28987–28996. iance data processing and harmonization was carried out by the Grundstein, A.J., Leathers, D.J., 1999. A spatial analysis of snow-surface energy ex- European Fluxes Database Cluster, AmeriFlux Management Project, and changes over the northern great plains of the United States in relation to synoptic scale forcing mechanisms. Int. J. Climatol. 19, 489–511. Fluxdata project of FLUXNET, with the support of CDIAC and ICOS Harding, R.J., Pomeroy, J.W., 1996. The energy balance of the winter boreal landscape. J. Ecosystem Thematic Center, and the OzFlux, ChinaFlux and AsiaFlux Clim. 9, 2778–2787. offices. PCS acknowledges support from the U.S. National Science Hawkins, T.W., Ellis, A.W., 2007. A case study of the energy budget of a snowpack in the arid, subtropical climate of the southwestern United States. J. Ariz. Nev. Acad. Sci. Foundation (DEB 1552976, OIA 1632810) and the USDA National 39, 1–13. Institute of Food and Agriculture Hatch project 228396. We thank Jon Hayashi, M., Hirota, T., Iwata, Y., Takayabu, I., 2005. Snowmelt energy balance and its – Evans and Colin Lloyd for work on Abisko eddy covariance data ac- relation to foehn events in Tokachi. Jpn. J. Meteorol. Soc. Jpn. 83, 783 798. Hommeltenberg, J., Schmid, H.P., Drösler, M., Werle, P., 2014. Can a bog drained for quisition and processing. Tobias Gerken provided valuable comments forestry be a stronger carbon sink than a natural bog forest? Biogeosciences 11, on earlier versions of this manuscript. We also thank the Natural 3477–3493. Environment Research Council (NERC) (award NE/D005922, PI M. Hood, E., Williams, M., Cline, D., 1999. Sublimation from a seasonal snowpack at a fi continental, mid-latitude alpine site. Hydrol. Process. 13, 1781–1797. Williams) for support of Abisko measurements. Any use of trade, rm, Hori, M., Aoiki, T., Tanikawa, T., Motoyoshi, H., Hachikubo, A., Sugiura, K., Yasunari, T., or product names is for descriptive purposes only and does not imply Eide, H., Storvold, R., Nakajima, Y., Takahashi, F., 2006. In-situ measured spectral endorsement by the U.S. Government. directional emissivity of snow and ice in the 8-14 μm atmospheric window. Remote Sens. Environ. 100, 486–502. Jocher, G., Ottosson Löfvenius, M., De Simon, G., Hörnlund, T., Linder, S., Lundmark, T., References Marshall, J., Nilsson, M.B., Näsholm, T., Tarvainen, L., Öquist, M., Peichl, M., 2017. Apparent winter CO2 uptake by a boreal forest due to decoupling. Agric. For. Meteorol. 232, 23–34. http://dx.doi.org/10.1016/j.agrformet.2016.08.002. Abatzoglou, J.T., Rupp, D.E., Mote, P.W., 2014. Seasonal climate variability and change Jonas, T., Rixen, C., Sturm, M., Stoeckli, V., 2008. How alpine plant growth is linked to in the Pacific Northwest of the United States. J. Clim. 27, 2125–2142. http://dx.doi. snow cover and climate variability. J. Geophys. Res: Biogeosci. 113, G03013. http:// org/10.1175/jcli-d-13-00218.1. dx.doi.org/10.1029/2007JG000680. Anthoni, P.M., Freibauer, A., Kolle, O., Schulze, E.-D., 2004. Winter wheat carbon ex- Julitta, T., Cremonese, E., Migliavacca, M., Colombo, R., Galvagno, M., Siniscalco, C., change in Thuringia. Ger. Agric. For. Meteorol. 121 (1-2), 55–67. Rossini, M., Fava, F., Cogliati, S., Morra di Cella, U., Menel, A., 2014. Using digital Arck, M., Scherer, D., 2002. Problems in the determination of sensible heat flux over camera images to analyse snowmelt and phenology of a subalpine grassland. Agric. snow. Geogr. Ann. Ser. Phys. Geogr. 84, 157–169. http://dx.doi.org/10.1111/j.0435- For. Meteorol. 198-199, 116–125. http://dx.doi.org/10.1016/j.agrformet.2014.08. 3676.2002.00170.x. 007. Aurela, M., Lohila, A., Tuovinen, J.P., Hatakka, J., Riutta, T., Laurila, T., 2009. Carbon Kaimal, J.C., Finnigan, J.J., 1994. Atmospheric Boundary Layer Flows: Their Structure dioxide exchange on a northern boreal fen. Boreal Environ. Res. 14, 699–710. and Measurement. Oxford University Press. Beaty, C.B., 1975. Sublimation or melting: observations from the white mountains, Kay, A.L., Crooks, S.M., 2014. An investigation of the effect of transient climate change on California and Nevada. U.S.A. J. Glaciol. 14, 275–286. http://dx.doi.org/10.1017/ snowmelt, flood frequency and timing in northern Britain. Int. J. Climatol. 34, S0022143000021766. 3368–3381. http://dx.doi.org/10.1002/joc.3913. Bedford, D., Douglass, A., 2008. Changing properties of snowpack in the Great Salt Lake Kottek, M., Grieser, J., Beck, C., Rudolf, B., Rubel, F., 2006. World map of the Köppen- Basin, western United States, from a 26-year SNOTEL record. Prof. Geogr. 60, Geiger climate classification updated. Meteorol. Z. 15, 259–263. http://dx.doi.org/ 374–386. 10.1127/0941-2948/2006/0130. Boike, J., 2003. Seasonal snow cover on frozen ground: energy balance calculations of a Liljedahl, A.K., Hinzman, L.D., Harazono, Y., Zona, D., Tweedie, C.E., Hollister, R.D., permafrost site near Ny-Ålesund, Spitsbergen. J. Geophys. Res. 108. http://dx.doi. Engstrom, R., Oechel, W.C., 2011. Nonlinear controls on evapotranspiration in arctic org/10.1029/2001JD000939. coastal wetlands. Biogeosciences 8, 3375–3389. Boon, S., 2009. Snow ablation energy balance in a dead forest stand. Hydrol. Process. 23, Loescher, H.W., Hanson, C.V., Ocheltree, T.W., 2009. The psychrometric constant is not 2600–2610. http://dx.doi.org/10.1002/hyp.7246. constant: a novel approach to enhance the accuracy and precision of latent energy Burns, S.P., Molotch, N.P., Williams, M.W., Knowles, J.F., Seok, B., Monson, R.K., fluxes through automated water vapor calibrations. J. Hydrometeorol. 10, Turnipseed, A.A., Blanken, P.D., 2014. Snow temperature changes within a seasonal 1271–1284. snowpack and their relationship to turbulent fluxes of sensible and latent heat. J. MacDonald, M.K., Pomeroy, J.W., Essery, R.L.H., 2018. Water and energy fluxes over Hydrometeorol. 15, 117–142. northern prairies as affected by chinook winds and winter precipitation. Agric. For. Campbell, G.S., Norman, J.M., 1998. An Introduction to Environmental Biophysics. Meteorol. http://dx.doi.org/10.1016/j.agrformet.2017.10.025. Springer New York, New York, NY. Mahrt, L., Vickers, D., 2005. Moisture fluxes over snow with and without protruding Cline, D.W., 1997. Snow surface energy exchanges and snowmelt at a continental, mid- vegetation. Q. J. R. Meteorol. Soc. 131, 1251–1270. http://dx.doi.org/10.1256/qj. latitude Alpine site. Water Resour. Res. 33, 689–701. http://dx.doi.org/10.1029/ 04.66. 97WR00026. Marcolla, B., Cescatti, A., Manca, G., Zorer, R., Cavagna, M., Fiora, A., Gianelle, D., Coughlan, J.C., Running, S.W., 1997. Regional ecosystem simulation: a general model for Rodeghiero, M., Sottocornola, M., Zampedri, R., 2011. Climatic controls and eco- simulating snow accumulation and melt in mountainous terrain. Landscape Ecol. 12, system responses drive the inter-annual variability of the net ecosystem exchange of 119–136. an alpine meadow. Agric. For. Meteorol. 151, 1233–1243. Marks, D., Dozier, J., 1992. Climate and energy exchange at the snow surface in the alpine Near‐surface remote sensing of spatial and temporal variation in canopy phenology. region of the Sierra Nevada: 2. Snow cover energy balance. Water Resour. Res. 28, Ecol. Appl. 19, 1417–1428. 3043–3054. http://dx.doi.org/10.1029/92WR01483. Serreze, M.C., Clark, M.P., Armstrong, R.L., McGinnis, D.A., Pulwarty, R.S., 1999. Marks, D., Winstral, A., 2001. Comparison of snow deposition, the snow cover energy Characteristics of the western United States snowpack from snowpack telemetry balance, and snowmelt at two sites in a semiarid mountain basin. J. Hydrometeorol. (SNOTEL) data. Water Resour. Res. 35, 2145–2160. 2, 213–227. http://dx.doi.org/10.1175/1525-7541(2001)002&0213:COSDTS&2.0. Slaughter, A.E., McCabe, D., Munter, H., Staron, P.J., Adams, E.E., Catherine, D., CO;2. Henninger, I., Cooperstein, M., Leonard, T., 2009. An investigation of radiation-re- Marks, D., Winstral, A., Flerchinger, G., Reba, M., Pomeroy, J., Link, T., Elder, K., 2008. crystallization coupling laboratory and field studies. Cold Reg. Sci. Technol. 59, Comparing simulated and measured sensible and latent heat fluxes over snow under a 126–132. http://dx.doi.org/10.1016/j.coldregions.2009.07.002. pine canopy to improve an energy balance snowmelt model. J. Hydrometeorol. 9, Spadavecchia, L., Williams, M., Bell, R., Stoy, P.C., Huntley, B., van Wijk, M.T., 2008. 1506–1522. http://dx.doi.org/10.1175/2008JHM874.1. Topographic controls on the leaf area index and plant functional type of a tundra Migliavacca, M., Galvagno, M., Cremonese, E., Rossini, M., Meroni, M., Sonnentag, O., ecosystem. J. Ecol. 96, 1238–1251. http://dx.doi.org/10.1111/j.1365-2745.2008. Cogliati, S., Manca, G., Diotri, F., Busetto, L., Cescatti, A., 2011. Using digital repeat 01424.x. photography and eddy covariance data to model grassland phenology and photo- Staebler, R.M., Fitzjarrald, D.R., 2004. Observing subcanopy CO2 advection. Agric. For. synthetic CO2 uptake. Agric. For. Meteorol 151, 1325–1337. Meteorol. 122, 139–156. http://dx.doi.org/10.1016/j.agrformet.2003.09.011. Misson, L., Baldocchi, D.D., Black, T.A., Blanken, P.D., Brunet, Y., Curiel Yuste, J., Dorsey, Stoy, P.C., Street, L.E., Johnson, A.V., Prieto-Blanco, A., Ewing, S.A., 2012. Temperature, J.R., Falk, M., Granier, A., Irvine, M.R., Jarosz, N., Lamaud, E., Launiainen, S., Law, heat flux, and reflectance of common subarctic mosses and lichens under field con- B.E., Longdoz, B., Loustau, D., McKay, M., Paw U, K.T., Vesala, T., Vickers, D., ditions: might changes to community composition impact climate-relevant surface Wilson, K.B., Goldstein, A.H., 2007. Partitioning forest carbon fluxes with overstory fluxes? Arct. Antarct. Alp. Res. 44, 500–508. http://dx.doi.org/10.1657/1938-4246- and understory eddy-covariance measurements: a synthesis based on FLUXNET data. 44.4.500. Agric. For. Meteorol. 144, 14–31. http://dx.doi.org/10.1016/j.agrformet.2007.01. Stoy, P.C., Williams, M., Evans, J.G., Prieto-Blanco, A., Disney, M., Hill, T.C., Ward, H.C., 006. Wade, T.J., Street, L.E., 2013. Upscaling tundra CO2 exchange from chamber to eddy Molotch, N.P., Blanken, P.D., Williams, M.W., Turnipseed, A.A., Monson, R.K., Margulis, covariance tower. Arct. Antarct. Alp. Res. 45, 275–284. http://dx.doi.org/10.1657/ S.A., 2007. Estimating sublimation of intercepted and sub-canopy snow using eddy 1938-4246-45.2.275. covariance systems. Hydrol. Process. 21, 1567–1575. http://dx.doi.org/10.1002/ Stoy, P.C., Quaife, T., 2015. Probabilistic downscaling of remote sensing data with ap- hyp.6719. plications for multi-scale biogeochemical flux modeling. PloS One 10, p.e0128935. Mott, R., Egli, L., Grünewald, T., Dawes, N., Manes, C., Bavay, M., Lehning, M., 2011. Street, L.E., Stoy, P.C., Sommerkorn, M., Fletcher, B.J., Sloan, V.L., Hill, T.C., Williams, Micrometeorological processes driving snow ablation in an Alpine catchment. The M., 2012. Seasonal bryophyte productivity in the sub-arctic: a comparison with Cryosphere 5, 1083–1098. http://dx.doi.org/10.5194/tc-5-1083-2011. vascular plants: seasonal bryophyte productivity in the sub-arctic. Funct. Ecol. 26, Mott, R., Gromke, C., Grunewald, T., Lehning, M., 2013. Relative importance of advective 365–378. http://dx.doi.org/10.1111/j.1365-2435.2011.01954.x. heat transport and boundary layer decoupling in the melt dynamics of a patchy snow Thomas, C.K., Martin, J.G., Law, B.E., Davis, K., 2013. Toward biologically meaningful cover. Adv. Water Resour. 55, 88–97. http://dx.doi.org/10.1016/j.advwatres.2012. net carbon exchange estimates for tall, dense canopies: multi-level eddy covariance 03.001. observations and canopy coupling regimes in a mature Douglas-fir forest in Oregon. Musselman, K.N., Clark, M.P., Liu, C., Ikeda, K., Rasmussen, R., 2017. Slower snowmelt in Agric. For. Meteorol. 173, 14–27. http://dx.doi.org/10.1016/j.agrformet.2013.01. a warmer world. Nat. Clim. Change 7, 214–219. http://dx.doi.org/10.1038/ 001. nclimate3225. Troin, M., Poulin, A., Baraer, M., Brissette, F., 2016. Comparing snow models under Owen, K.E., Tenhunen, J., Reichstein, M., Wang, Q., Falge, E., Geyer, R., Xiao, X., Stoy, current and future climates: uncertainties and implications for hydrological impact P.C., Amman, C., Arain, A., Aubinet, M., Aurela, M., Bernhofer, C., Chojnicki, B., studies. J. Hydrol. 540, 588–602. http://dx.doi.org/10.1016/j.jhydrol.2016.06.055. Granier, A., Gruenwald, T., Hadley, J., Heinesch, B., Hollinger, D., Knohl, A., Kutsch, Verma, S.B., Dobermann, A., Cassman, K.G., 2005. Annual carbon dioxide exchange in W., Laurila, T., Lohila, A., Meyers, T., Moors, E., Moureaux, C., Verma, S., Vesala, T., irrigated and rainfed maize-based agroecosystems. Agric. For. Meteorol. 131, 77–96. Vogel, C.S., 2007. Linking flux network measurements to continental scale simula- Warren, S.G., 1984. Impurities in snow: effects on albedo and snowmelt. Ann. Glaciol. 5, tions: ecosystem carbon dioxide exchange capacity under non-water- stressed con- 177–179. ditions. Global Change Biol. 13, 734–760. Welch, C.M., Stoy, P.C., Rains, F.A., Johnson, A.V., McGlynn, B.L., 2016. The impacts of Pastorello, G.Z., Papale, D., Chu, H., Trotta, C., Agarwal, D.A., Canfora, E., Baldocchi, mountain pine beetle disturbance on the energy balance of snow during the melt D.D., Torn, M.S., 2017. A new data set to keep a sharper eye on land-air exchanges. period: snowmelt response to mountain pine beetle disturbance. Hydrol. Process. 30 Eos Trans. AGU 98. http://dx.doi.org/10.1029/2017EO071597. (4), 588–602. http://dx.doi.org/10.1002/hyp.10638. Pederson, G.T., Betancourt, J.L., McCabe, G.J., 2013. Regional patterns and proximal Wever, N., Vera Valero, C., Fierz, C., 2016. Assessing wet snow avalanche activity using causes of the recent snowpack decline in the rocky mountains, U.S.: proximal causes detailed physics based snowpack simulations. Geophys. Res. Lett. 43, 5732–5740. of snowpack declines. Geophys. Res. Lett. 40, 1811–1816. http://dx.doi.org/10. http://dx.doi.org/10.1002/2016gl068428. 1002/grl.50424. Wohlfahrt, G., Hammerle, A., Haslwanter, A., Bahn, M., Tappeiner, U., Cernusca, A.,

Pederson, G.T., Gray, S.T., Woodhouse, C.A., Betancourt, J.L., Fagre, D.B., Littell, J.S., 2008. Seasonal and inter-annual variability of the net ecosystem CO2 exchange of a Watson, E., Luckman, B.H., Graumlich, L.J., 2011. The unusual nature of recent temperate mountain grassland: effects of weather and management. J. Geophys. Res. snowpack declines in the North American Cordillera. Science 333 (6040), 332–335. 113 (D8), D08110. http://dx.doi.org/10.1126/science.1201570. Wiscombe, W.J., Warren, S.G., 1980. A model for the spectral albedo of snow. I: pure Pohl, S., Marsh, P., Liston, G.E., 2006. Spatial-temporal variability in turbulent fluxes snow. J. Atmos. Sci. 37, 2712–2733. during spring snowmelt. Arct. Antarct. Alp. Res. 38, 136–146. Zeeman, M.J., Mauder, M., Steinbrecher, R., Heidbach, K., Eckart, E., Schmid, H.P., 2017. Reba, M.L., Link, T.E., Marks, D., Pomeroy, J., 2009. An assessment of corrections for Reduced snow cover affects productivity of upland temperate grasslands. Agric. For. Eddy covariance measured turbulent fluxes over snow in mountain environments: Meteorol. 232, 514–526. http://dx.doi.org/10.1016/j.agrformet.2016.09.002. Eddy covariance over snow in mountain environments. Water Resour. Res. 45. Zhu, G., He, Y., Pu, T., Wang, X., Jia, W., Li, Z., Xin, H., 2012. Spatial distribution and http://dx.doi.org/10.1029/2008WR007045. temporal trends in potential evapotranspiration over Hengduan Mountains region Richardson, A.D., Braswell, B.H., Hollinger, D.Y., Jenkins, J.P., Ollinger, S.V., 2009. from 1960 to 2009. J. Geogr. Sci. 22, 71–85.